Classifying critical points

True (only one max y value, can have multiple x values)

A continuous function on a closed interval can have only one maximum values

False (x^3)

A critical point of a function f of a variable x is the x coordinate of a relative min or max

True

Absolute extrema of a continuous function on a closed intervals can occur at only endpoints or critical points

When you see and f'(#)=0 what should you think

Critical number

False (absolute value function

If a function f had a relative minimum at x=c. Then f prime c is zero

True

If a function f is defined on a closed interval and f'(x)>0 for all x in the interval, then the absolute maximum will occur at the RIGHT endpoint of the interval

False (f prime must be 0)

If f double prime is always positive the function f must have a relative minimum value

False.If f''(c)=0, then x=c MAY OR MAY NOT BE a point of inflection for the function f and MAY OR MAY NOT be the x coordinate of a max or min point in the graph of f

If f''(c)=0, then x=c is a point of inflection for the function f and cannot be the x coordinate of a max or min point in the graph of f

True

If f'(2)=0 and f''(2)<0, then x=2 locates a relative maximum value of f

False (relative max)

If f'(c)=0 and f'(x) decreases through x=c, then x=c locates a relative min value of the function

True

If x=2 is the only critical point of a function f and f''(2)>0, then f(2) is the minimum value of the function

False (repeating graphs like f(x)=sinx

The absolute minimum of a continuous function on a closed interval can occur at only one point

False (and endpoints)

To locate the absolute extrema of a continuous function on a closed interval, you need only compare the y values of all critical points